Robust allele-sharing linkage analysis methods have a crucial role in the search for disease susceptibility loci involved in genetically complex diseases. These methods achieve their robustness by directly testing for non-random segregation of markers to affected individuals, instead of making indirect inferences about recombination. We will extend existing theory to develop allele-sharing statistics that are powerful even when little is known about the mode of inheritance of a trait. We will include statistics for: i) affected relative pairs and inbred individuals; ii) pedigrees with three or more affecteds; iii) affected and unaffected individuals; iv) combining pedigrees; v) explicit searches for multiple loci; vi) explicit searches for gene- environment interactions; and vii) array data with significant error rates. Application of such statistics to family data sets typed for many markers requires use of a computational engine for estimating the underlying identity-by-descent sharing of the markers. One promising approach to these computations is the Markov chain Monte Carlo (MCMC) methods, which can handle previously intractable data sets. We plan to develop and extend an MCMC computational engine to: i) carry out rapid computation of multipoint identity-by-descent matrices; ii) perform conditional simulation studies; iii) perform haplotype analysis; iv) perform exact computations on small pedigrees and approximate computations on large pedigrees; v) compute multipoint location scores; and vi) perform computations with array data as well as with traditional genotype data. We will combine our computational engine with our robust theories to provide a comprehensive software package. We will evaluate this package rigorously via well-designed simulation studies which will measure the power and false-positive rates of our new statistics. After creating an interactive graphical user-interface, we will distribute our software with documentation, via the Internet, to the world-wide scientific community.